Measurement Techniques, Vol. 37, No. 1, 1994 FUNDAMENTAL PROBLEMS OF METROLOGY SIMULATION OF THE PROCEDURE FOR MEASURING THE GRAVITATIONAL CONSTANT ON AN EARTH SATELLITE A. D. Alekseev, K. A. Bronnikov, N. I. Kolosnitsyn, V. N. Md'nikov, and A. G. Radynov UDC 681.2.08:528.27/.083 A simulation is described for measuring the newtonian gravitational constant G in the SEE space experiment. Two methods are examined for estimating G: the two-point method and the integral one. When the two-point method is used, to provide an error not more than AG/G = 1"10 -6 requires path measurements to be performed with an error of not more than 1.10 -8 m = k/50 CA is the green line wavelength). In the integral method, the same error in estimating G is attained with an error of measurement different by two orders of magnitude, 1.10 -6 m. METHODS OF DETERMINING THE GRAVITATIONAL CONSTANT This paper continues [I, 2], which dealt with a method of determining the gravitational constant G in a space laboratory [3], with the Satellite Energy Exchange (SEE) method. The study is performed for a circular orbit in the approximation of a spherically symmetricaI newtonian potential GME/r. The motion of a small body (particle) is considered within the framework of the three-body problem, which includes the Earth and the leading body in the herd. We assume that the particle moves in the orbital relative to the herd from the standard equations for the motion of many bodies [4]. These equations are as follows in the coordinate system having its origin at the center of the herd: 92 ---x--3o3~x-~ - - 3(x2--y2!2)=O ; t'O1 G(mxq-m2) o~ (l) -- 3xg=0, yq.-2~x-'l- 9s --y-- r0x where m 1 and m 2 are correspondingly the masses of the herd and the particle, and p=(x2q-y2)l/2 ; o~=GME ]r~l ; rot~-a-4-H; with a the mean equatorial radius and H the height of the equatorial orbit. The product of the gravitational constant and the Earth's mass GM is known very accurately. The x axis is directed along the radius vector of the center of mass of the herd, and the y axis is along the tangent to the path. There are three methods of determining G, which we call the differential one, the two-point one, and the integral one. Differential Method. This is based on estimating G directly from the (1) differential equations. The input data are represented by the set of known parameters mr, m2, GME, a, and H together with the set of coordinates of the particle x i and Yi as measured at the times t i. The second derivatives in (1) are estimated by standard methods from x i, Yi, and t i. Advantages Translated from Izmeritel'naya Tekhnika, No. 1, pp. 3-5, January, 1994. 0543-1972/94/3701-0001512.50 9 Plenum Publishing Corporation 1